In recent years, with the appearance of “turbo principle” (“Near shannon limit error-correcting coding and decoding: Turbo-codes”, C. BEROU), iterative receivers are popular and capable because of their excellent performances.
Different mechanisms have been proposed and studied, for example, iterative detection, iterative multi-input multi-output (MIMO) equalization, etc. However, these iterative mechanisms are seriously affected by channel estimator.
For example, in “Performance Analysis of Iterative Receiver in 3GPP/LTE DL MIMO OFDMA System” (L. BOHER et Al.), it has been shown that an iterative MIMO equalizer is more sensitive to channel estimation, and that the traditional non-iterative channel estimators cannot provide sufficiently accurate channel estimates. This necessitates more accurate channel estimates in order to improve system performances.
Recently, iterative channel estimation is being considered to improve the accuracy of channel estimation, which uses the “soft” information of data to improve channel estimation performance (soft information stands for information which is calculated along the iterative process, and which is used for the following iteration). This type of channel estimation algorithms is particularly helpful for systems which have fewer and/or lower powered pilot symbols. For example, in Long Term Evolution (LTE) systems, at most 2 orthogonal frequency-division multiplexing (OFDM) symbols carry pilots in a given resource block (RB=minimum allocation unit over 7 OFDM symbols with normal cyclic prefix and 12 subcarriers) and this can decrease to 1 OFDM symbols for MIMO transmission (3GPP, “Evolved universal terrestrial radio access (E-UTRA); physical channels and modulation”, available at http://www.3gpp.org/ftp/Specs/html-info/36211.htm), thus defining a so called “sparse pilot arrangement”.
With this sparse pilot arrangement, the iterative channel estimation can be a good candidate to improve channel estimation. Moreover, for future standards, one of the key features will be power efficiency and, in this manner, decreasing the power of pilots is one of the possible ways to improve the power consumption efficiency. In such systems, the channel estimation algorithms used in nowadays systems will have less accuracy and more robust algorithms are needed.
Some iterative channel estimators have already been proposed for OFDM systems by using the extrinsic information from decoder. Among these iterative algorithms, the iterative minimum mean square error (MMSE) channel estimator provides excellent performances which approach the performance with perfect channel state information (CSI).
The iterative MMSE is based on the traditional MMSE channel estimator defined in “On channel estimation in OFDM systems” (J.-J. van de Beek et Al.) and improves the accuracy of channel estimation by using the soft information obtained from channel decoder. In the frequency domain, the traditional iterative MMSE channel estimation at the i+1th iteration ĥMMSE(i+1) can be MMSE formulized as:ĥMMSE(i+1)=ΩL(ΩLH{tilde over (R)}N×N(i)ΩL+σ2Cgg−1)−1ΩLH{tilde over (X)}(i)*y,  (1)where (•)H stands for transpose-conjugate and (•)* stands for complex conjugate.
Here, y stands for the received signal vector, ΩL is a matrix consisting of the first L (L representing the delay spread of channel) columns of the FFT matrix, {tilde over (X)}(i) represents a diagonal matrix which has soft symbols {tilde over (X)}kk(i) as diagonal entries, which contain the a posteriori probabilities (APPs) of the data Xkk at the ith iteration, ĥMMSE(i+1) is the estimated channel vector at the (i+1)th iteration, the matrix {tilde over (R)}N×N(i) is defined as:
                                                        R              ~                                      N              ×              N                                      (              i              )                                =                                    ∑              X                        ⁢                                                            APP                  i                                ⁡                                  (                  X                  )                                            ⁢                                                X                  ~                                                                      (                    i                    )                                    *                                            ⁢                                                X                  ~                                                  (                  i                  )                                                                    ;                            (        2        )            Cgg is the auto-covariance matrix of impulse response g and σ2 denotes the noise variance. In equation (1), the complexity of the iterative MMSE channel estimator is high due to the matrix inversion of size L×L which has to be performed at each iteration of the estimation process.
Furthermore, in LTE systems, the distributed resource allocation is used to vary resources blocks (RB) positions in different OFDM symbols. With the iterative MMSE algorithm, the allocated RB positions have to be pinpointed and the matrix to be inverted is different from one OFDM symbol to another one.
This process adds more complexities to the iterative MMSE algorithm. Therefore, an iterative MMSE algorithm which is not sensitive to RB positions is more desirable because of its reduced complexity.
Thus, it is important to propose a channel estimation algorithm in which the complexity of the calculation is reduced in order to shorten latency time.
For clarity purposes, it is further noted that, in the present description, a capital letter (like H, R, X) represents a matrix whereas a lower case letter (like h, y, . . . ) represents a vector (i.e. a matrix with a single row). For example, h represents channel estimates in Frequency Domain and it is a vector. It is also specified that the expression “a channel estimate” is a value which is the result of “a channel estimation”. (the noun “estimate” means a estimated value and the noun “estimation” means the action for obtaining an estimate).